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Mathematics
On one scenario for changing the stability of invariant manifolds of singularly perturbed systems
O. S. Kipkaeva Samara National Research University, Samara, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The article is devoted to the peculiarities of stability change of slow invariant manifolds of singularly perturbed systems of ordinary differential equations. It should be noted that the change of stability of invariant manifolds can proceed according to different scenarios. In addition to two well-known scenarios of this phenomenon, one more scenario is considered in this paper. To demonstrate the peculiarities of the stability change of slow invariant manifolds under this scenario, a number of examples are proposed. The existence theorem of an exact invariant manifold with stability change for some class of singularly perturbed systems of ordinary differential equations is obtained.
Keywords:
dynamical systems, singular perturbations, invariant manifolds, stability, delayed stability loss, canards, bifurcation, existence theorem.
Received: 21.01.2024 Revised: 17.04.2024 Accepted: 15.05.2024
Citation:
O. S. Kipkaeva, “On one scenario for changing the stability of invariant manifolds of singularly perturbed systems”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 30:2 (2024), 20–29
Linking options:
https://www.mathnet.ru/eng/vsgu736 https://www.mathnet.ru/eng/vsgu/v30/i2/p20
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Abstract page: | 20 | Full-text PDF : | 5 | References: | 10 |
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